Days of Week Permutation Listing

[Steve Morris]

I am trying to create a list of all possible days of week possibilities. It appears that there are over 5,000 variations based on the permutation. The goal is to provide a reference of each possible scenario based on a "1" representing the actual day referenced.

The enclosed spreadsheet shows the pattern that I am trying to develop that would be a table for a vlookup from reports that indicate a day of service by the number "1". Developing every possibility with the string of 7 digits that can also be converted to the day initials. The initial would be the first letter of the week with H being Thursday and U being
Sunday.

 

[Hui]

Isn't there only 127 combinations?

See attached solution

Column I drives the calculations

 

[Steve Morris]

Isn't there only 127 combinations?

Not if you take every variation (i.e. MTHS, THSU, MU, MWHFSU, etc.).

 

[Hui]

Please see my revised post above

 

[NARAYANK991]

Hi ,

It is not very clear what you want to do.

Can we first describe the problem without any reference to your workbook ?

There are 7 days in a week ; we can represent them by the letters :

M - Monday

T - Tuesday

W - Wednesday

H - Thursday

F - Friday

S - Saturday

U - Sunday

If you really mean permutation , where order is important , then we can have 7! ( 7 factorial ) different permutations , which equals 5040 , assuming that we are using all 7 days of the week for every permutation.

Thus starting with the first permutation , which can be the natural calendar order , we will have the permutation MTWHFSU ; the last permutation can be the fully reversed order of USFHWTM.

These 5040 permutations cannot be derived from the binary representation of 1s and 0s , since if we are going to have only 7 ones and zeros , the maximum number that we can achieve using 7 binary digits is 2 raised to the power 7 , which is 128.

Secondly , if you are going to include even other combinations such as the 7 days on their own , permutations of 2 days at a time , permutations of 3 days at a time , and so on , then the total number possible is much more than 5040.

If you can explain what exactly you want to do , without any reference to your uploaded workbook , then a more elegant data representation and solution can be arrived at.

Narayan

 

[Hui]

Whoops there was small mistake above
Corrected below

 

[Hui]

You may also be interested in:
https://sites.google.com/site/e90e50fx/home/combinatorics-using-excel-formulas-and-examples

 

[Steve Morris]

Whoops there was small mistake above
Corrected below

The corrected version will get the job done since it only needs to contain the day and not necessarily in a specific order. I ran the permutation formula and assumed the 5,000 was correct.

Thanks for all of your help with this.